KLOE-MAMI η\!→\!π⁰γγ Puzzle Solution via Nucleon-Rescaled Leptophobic Vector from Scalar Portal

The recent KLOE measurement BR^η→π⁰γγKLOE = (0.98±0.11ₛₜₐₜ±0.14syst)×10⁻⁴ is less than half the current world average, (2.55±0.22)×10⁻⁴, which is dominated by MAMI photoproduction data. We show that this ≈ 5.5\, σ discrepancy can be resolved by the presence of a new leptophobic vector particle VB with 2\ GeV m_V\! B 5\ GeV, whose couplings arise through the GeV-scale scalar portal. Integrating out the scalar generates the contact operator ( N N)\, VBμνFμνP that modifies the η⁽⁾\!→\!π⁰(η)γγ decay rate only in the processes involving an external nucleon current (γp\!→\!η⁽⁾p, π⁻p\!→\!η⁽⁾n), but leaves purely leptonic production channels, such as ϕ→ηγ at KLOE and J/ψ→γη at BESIII, Standard-Model-like. The same mechanism predicts a ≈ 10% nucleon-triggered enhancement of the η'\!→\!π⁰γγ decay rate and a negligible shift for η'\!→\!ηγγ, together with an A²-scaling boost if photoproduction is performed on heavy nuclei instead of protons. An integrated experimental programme that compares η⁽⁾ → η(π⁰) γγ decays in the presence of nucleon currents, as opposed to purely leptonic production channels, searches for a narrow nucleon-philic vector in the 2\!-\!5\,GeV mass range, and probes scalar portals above 1\,GeV, can decisively confirm or exclude our nucleon-rescaled, leptophobic-vector explanation of the KLOE-MAMI discrepancy.